Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series B, Pt. 2, pp. 234--249

BAMS METHOD: THEORY AND SIMULATIONS

By

BRANI VIDAKOVIC Georgia Institute of Technology, Atlanta

and

FABRIZIO RUGGERI CNR-IAMI, Milano

SUMMARY. In this paper we address the problem of model-induced wavelet shrinkage. Assuming the independence model according to which the wavelet coefficients are treated individually, we discuss a level-adaptive Bayesian model in the wavelet domain that has two important properties: (i) it realistically describes empirical properties of signals and images in the wavelet domain, and (ii) it results in simple optimal shrinkage rules to be used in fast wavelet denoising. The proposed denoising paradigm BAMS (short for Bayesian Adaptive Multiresolution Shrinker) is illustrated on an array of Donoho and Johnstone's standard test functions and is compared to some standard wavelet-based smoothing methods.

AMS (2000) subject classification. Primary 65T60; secondary 62F15.

Key words and phrases. Wavelet regression, shrinkage, adaptivity, denoising.

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